Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 284, Issue -, Pages 102-114Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2016.02.055
Keywords
Simultaneous methods; Polynomial zeros; Semilocal convergence; Error estimates; Ehrlich method; Dochev-Byrnev method
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In this paper, we establish a general semilocal convergence theorem (with computationally verifiable initial conditions and error estimates) for iterative methods for simultaneous approximation of polynomial zeros. As application of this theorem, we provide new semilocal convergence results for Ehrlich's and Dochev-Byrnev's root-finding methods. These results improve the results of Petkovic et al. (1998) and Proinov (2006). We also prove that Dochev- Byrnev's method (1964) is identical to Presic-Tanabe's method (1972). (C) 2016 Elsevier Inc. All rights reserved.
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